We study the problem of learning-based attacks in linear systems, where the communication channel between the controller and the plant can be hijacked by a malicious attacker. We assume the attacker learns the dynamics of the system from observations, then overrides the controller's actuation signal, while mimicking legitimate operation by providing fictitious sensor readings to the controller. On the other hand, the controller is on a lookout to detect the presence of the attacker and tries to enhance the detection performance by carefully crafting its control signals. We study the trade-offs between the information acquired by the attacker from observations, the detection capabilities of the controller, and the control cost. Specifically, we provide tight upper and lower bounds on the expected $\epsilon$-deception time, namely the time required by the controller to make a decision regarding the presence of an attacker with confidence at least $(1-\epsilon\log(1/\epsilon))$. We then show a probabilistic lower bound on the time that must be spent by the attacker learning the system, in order for the controller to have a given expected $\epsilon$-deception time. We show that this bound is also order optimal, in the sense that if the attacker satisfies it, then there exists a learning algorithm with the given order expected deception time. Finally, we show a lower bound on the expected energy expenditure required to guarantee detection with confidence at least $1-\epsilon \log(1/\epsilon)$.

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网络物理系统中基于学习的攻击：探索，检测和控制成本的权衡

我们研究线性系统中基于学习的攻击的问题，其中控制器和工厂之间的通信通道可能被恶意攻击者劫持。我们假设攻击者从观察中了解系统的动态，然后覆盖控制器的驱动信号，同时通过向控制器提供虚拟传感器读数来模仿合法操作。另一方面，控制器正在监视以检测攻击者的存在，并通过精心制作其控制信号来尝试提高检测性能。我们研究了攻击者从观察中获得的信息，控制器的检测能力以及控制成本之间的权衡。具体来说，我们为预期的\ epsilon $-欺骗时间提供了严格的上限和下限，就是说，控制器至少有$（1- \ epsilon \ log（1 / \ epsilon））$来决定是否存在攻击者所需的时间。然后，我们显示了攻击者学习系统所必须花费的时间的概率下限，以使控制器具有给定的预期\ epsilon $-欺骗时间。我们表明，从一定程度上讲，如果攻击者满足要求，那么该边界也是有序最优的，那么就存在一种具有给定阶数预期欺骗时间的学习算法。最后，我们给出了保证至少有$ 1- \ epsilon \ log（1 / \ epsilon）$置信度所需的预期能量消耗的下限。然后，我们显示了攻击者学习系统所必须花费的时间的概率下限，以使控制器具有给定的预期\ epsilon $-欺骗时间。我们表明，从一定程度上讲，如果攻击者满足要求，那么该边界也是有序最优的，那么就存在一种具有给定阶数预期欺骗时间的学习算法。最后，我们给出了保证至少有$ 1- \ epsilon \ log（1 / \ epsilon）$置信度所需的预期能量消耗的下限。然后，我们显示了攻击者学习系统所必须花费的时间的概率下限，以使控制器具有给定的预期\ epsilon $-欺骗时间。我们表明，从一定程度上讲，如果攻击者满足要求，那么该边界也是有序最优的，那么就存在一种具有给定阶数预期欺骗时间的学习算法。最后，我们给出了保证至少有$ 1- \ epsilon \ log（1 / \ epsilon）$置信度所需的预期能量消耗的下限。